But the King County Police Officers Guild, which represents sheriff’s deputies, told county officials Thursday it won’t give up next year’s 5 percent raise guaranteed in its five-year contract, county spokesman Frank Abe said.

If deputies had agreed to give up their raise, the Sheriff’s Office would have saved more than $3 million, budget officials said, and likely would have prevented any layoffs.

Sheriff Sue Rahr has given layoff notices to 28 deputies and two civilian employees, and says she plans to fill 51 vacant positions by returning supervisors and detectives to lower-paid patrol duties.

Representatives of the Police Officers Guild could not be reached for comment Thursday.

County Executive Dow Constantine will tell the Metropolitan King County Council on Monday how he plans to deal with a projected $60 million general-fund shortfall caused by rising expenses combined with plummeting property- and sales-tax revenues.

Constantine’s budget office has told the sheriff and prosecutor to plan for cuts of more than 9 percent from the cost to maintain existing programs.

Constantine has pledged to restore criminal-justice programs if voters on Nov. 2 approve King County Proposition 1, a two-tenths of a cent increase in the sales tax on a $1 purchase.

The tax measure would also replace the dilapidated Youth Services Center courthouse in Seattle. Cities would receive 40 percent of the tax proceeds. Satterberg is a strong advocate of the sales tax.

Since he took office three years ago after the death of his friend and supervisor, longtime prosecutor Norm Maleng, Satterberg has eliminated the positions of 20 prosecutors and seven support staffers through layoffs and unfilled vacancies.

The next round of layoffs would leave the prosecutor’s office with about 220 deputy prosecutors — 40 fewer than when he took office.

The last time prosecutors were laid off, Satterberg’s office began referring many felony property crimes to district or municipal court prosecutors and offering misdemeanor plea deals to defendants in other property-crime or drug-possession cases.

Easing filing standards wouldn’t be appropriate for other kinds of felonies his office handles, Satterberg said, but some white-collar theft, financial abuse of elders and cold-case murders, may have to go “on the back burner” if they are too time-consuming and complicated.

And with fewer prosecutors available to handle trials, they will feel pressure to settle more cases through plea deals. “My fear is if we lack sufficient deputy prosecutors to be in the courtroom, we lose the credible threat of trial in order to get a good plea resolution,” Satterberg said.

He said budget cuts won’t affect the prosecution of murders, rapes and aggravated assaults and other violent crimes.